How many ounces of a 19% copper alloy metal must be added to 42% ounces of a 40% copper alloy metal to produce a metal which is 31% copper alloy
To solve this problem, let's break it down step by step.
Step 1: Define the variables:
Let's call the unknown quantity of 19% copper alloy metal x ounces.
The given quantity of 42% copper alloy metal is already provided as 40 ounces.
Step 2: Set up the equation:
The equation can be set up based on the mass and percentage of copper in each alloy.
For the copper content:
0.19x (amount of copper in 19% alloy metal) + 0.42(40) (amount of copper in 42% alloy metal) = 0.31(x + 40) (amount of copper in final 31% alloy metal)
Step 3: Solve the equation:
Now we can solve the equation to find the value of x.
0.19x + 16.8 = 0.31x + 12.4
0.12x = 4.4
x = 4.4 / 0.12
x ≈ 36.67
So, approximately 36.67 ounces of the 19% copper alloy metal must be added to 40 ounces of the 42% copper alloy metal to produce a metal that is 31% copper alloy.